Question

Can someone please help me????

Answer 1

Answer: OPTION D

Step-by-step explanation:

Given the functions f(x) and g(x) shown in the figure attached, you have that g(x)-f(x) means that you must subtract both functions.

Therefore, keeping this on mind, you have:

$g(x)-f(x)=3x^{3}-x^{2}+7x-(x^{2}+3x+5)$

Now, you must distributive the negative sign that is in front of the parentheses and add the like terms. Then, you obtain:

$g(x)-f(x)=3x^{3}-x^{2}+7x-x^{2}-3x-5\\g(x)-f(x)=3x^{3}-2x^{2}+4x-5$

Answer 2

Answer:

$\boxed{D. \ g(x)-f(x)=3x^3-2x^2+4x-5}$

Step-by-step explanation:

We have two functions, namely:

$f(x)=x^2+3x+5 \ and \\ \\ g(x)=3x^3-x^2+7x$

So we need to subtract f(x) from g(x) and this is as follows:

$g(x)-f(x)=3x^3-x^2+7x-(x^2+3x=5) \\ \\ \therefore g(x)-f(x)=3x^3-x^2+7x-x^2-3x-5 \\ \\ By \ grouping \ equal \ terms: \\ \\ \therefore g(x)-f(x)=3x^3+(-x^2-x^2)+(7x-3x)-5 \\ \\ Solving: \\ \\ \boxed{g(x)-f(x)=3x^3-2x^2+4x-5}$